3(x+2)(x-5)=2x-8

Solution for 3(x+2)(x-5)=2x-8 equation:

Simplifying
3(x + 2)(x + -5) = 2x + -8

Reorder the terms:
3(2 + x)(x + -5) = 2x + -8

Reorder the terms:
3(2 + x)(-5 + x) = 2x + -8

Multiply (2 + x) * (-5 + x)
3(2(-5 + x) + x(-5 + x)) = 2x + -8
3((-5 * 2 + x * 2) + x(-5 + x)) = 2x + -8
3((-10 + 2x) + x(-5 + x)) = 2x + -8
3(-10 + 2x + (-5 * x + x * x)) = 2x + -8
3(-10 + 2x + (-5x + x2)) = 2x + -8

Combine like terms: 2x + -5x = -3x
3(-10 + -3x + x2) = 2x + -8
(-10 * 3 + -3x * 3 + x2 * 3) = 2x + -8
(-30 + -9x + 3x2) = 2x + -8

Reorder the terms:
-30 + -9x + 3x2 = -8 + 2x

Solving
-30 + -9x + 3x2 = -8 + 2x

Solving for variable 'x'.

Reorder the terms:
-30 + 8 + -9x + -2x + 3x2 = -8 + 2x + 8 + -2x

Combine like terms: -30 + 8 = -22
-22 + -9x + -2x + 3x2 = -8 + 2x + 8 + -2x

Combine like terms: -9x + -2x = -11x
-22 + -11x + 3x2 = -8 + 2x + 8 + -2x

Reorder the terms:
-22 + -11x + 3x2 = -8 + 8 + 2x + -2x

Combine like terms: -8 + 8 = 0
-22 + -11x + 3x2 = 0 + 2x + -2x
-22 + -11x + 3x2 = 2x + -2x

Combine like terms: 2x + -2x = 0
-22 + -11x + 3x2 = 0

Begin completing the square.  Divide all terms by
3 the coefficient of the squared term: 

Divide each side by '3'.
-7.333333333 + -3.666666667x + x2 = 0

Move the constant term to the right:

Add '7.333333333' to each side of the equation.
-7.333333333 + -3.666666667x + 7.333333333 + x2 = 0 + 7.333333333

Reorder the terms:
-7.333333333 + 7.333333333 + -3.666666667x + x2 = 0 + 7.333333333

Combine like terms: -7.333333333 + 7.333333333 = 0.000000000
0.000000000 + -3.666666667x + x2 = 0 + 7.333333333
-3.666666667x + x2 = 0 + 7.333333333

Combine like terms: 0 + 7.333333333 = 7.333333333
-3.666666667x + x2 = 7.333333333

The x term is -3.666666667x.  Take half its coefficient (-1.833333334).
Square it (3.361111114) and add it to both sides.

Add '3.361111114' to each side of the equation.
-3.666666667x + 3.361111114 + x2 = 7.333333333 + 3.361111114

Reorder the terms:
3.361111114 + -3.666666667x + x2 = 7.333333333 + 3.361111114

Combine like terms: 7.333333333 + 3.361111114 = 10.694444447
3.361111114 + -3.666666667x + x2 = 10.694444447

Factor a perfect square on the left side:
(x + -1.833333334)(x + -1.833333334) = 10.694444447

Calculate the square root of the right side: 3.270236145

Break this problem into two subproblems by setting 
(x + -1.833333334) equal to 3.270236145 and -3.270236145.

Subproblem 1
x + -1.833333334 = 3.270236145

Simplifying
x + -1.833333334 = 3.270236145

Reorder the terms:
-1.833333334 + x = 3.270236145

Solving
-1.833333334 + x = 3.270236145

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '1.833333334' to each side of the equation.
-1.833333334 + 1.833333334 + x = 3.270236145 + 1.833333334

Combine like terms: -1.833333334 + 1.833333334 = 0.000000000
0.000000000 + x = 3.270236145 + 1.833333334
x = 3.270236145 + 1.833333334

Combine like terms: 3.270236145 + 1.833333334 = 5.103569479
x = 5.103569479

Simplifying
x = 5.103569479

Subproblem 2
x + -1.833333334 = -3.270236145

Simplifying
x + -1.833333334 = -3.270236145

Reorder the terms:
-1.833333334 + x = -3.270236145

Solving
-1.833333334 + x = -3.270236145

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '1.833333334' to each side of the equation.
-1.833333334 + 1.833333334 + x = -3.270236145 + 1.833333334

Combine like terms: -1.833333334 + 1.833333334 = 0.000000000
0.000000000 + x = -3.270236145 + 1.833333334
x = -3.270236145 + 1.833333334

Combine like terms: -3.270236145 + 1.833333334 = -1.436902811
x = -1.436902811

Simplifying
x = -1.436902811

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.103569479, -1.436902811}